تكملة 6 
A nut initially at A on the screw will move up to B when rotated 360° 
around the screw
? This rotation is equivalent to translating the nut up an inclined plane of 
height l and length 2?r, where r is the mean radius of the head

? The rise l for a single revolution is referred to as the lead of 
the screw, where the lead angle is given by ? = tan-1 (l/2?r).

Frictional Analysis

? When a screw is subjected to large axial loads, the frictional forces developed on the thread become important to determine the moment M* needed to turn the screw. 

? Consider the square-threaded jack which supports vertical 
load W.
Upward Screw Motion:
? Relative forces of the jack to this load are distributed over the
circumference of the screw thread in contact with the screw
hole in the jack, that is, with in the region h
? For simplicity, the thread can represented by a simple block
resting on an inclined plane having screw’s lead angle ?.
Upward Screw Motion:
? The inclined plane represents the inside supporting thread of 
the jack base.
? 3 forces act on the block or screw.
? Force W is the total axial load applied to the screw.
? Horizontal force S is caused by the applied moment M such 
that by summing the moments about the axis of the screw, 
M = Sr where r is the screw’s mean radius.

? As a result of W and S, the inclined plane exerts a resultant R on the block, which is shown to have components acting normal, 
N, and tangent F, to the contacting surfaces.

? Provided M is large, the screw and the block can either be
brought to the verge of upward impending motion or motion can
be occurring 
? R acts at an angle (? + ?) from the vertical ? = tan-1 (F/N) = 
tan-1 (?N/N) = tan-1?